Belt Pulley

Library

Couplings & Drives

Description

This block represents a pulley wrapped in a flexible flat band
or V-shaped belt. The model accounts for friction between the flexible
belt and the pulley periphery. If the friction force is not sufficient
to drive the load, the model allows slip. The relationship between
the tensions in the tight and loose branches conforms to the Euler
equation. The model accounts for centrifugal loading in the flexible
belt, pulley inertia, and bearing friction.

The block dialog box enables you to select the relative belt
direction of motion. Depending on the chosen setting, the two belt
ends can move in equal or opposite directions. The block model assumes
noncompliance in the belt and no resistance to motion due to wrapping
around the pulley.

The Belt Pulley block uses the following equations to calculate
friction force:

Vrel is
the relative velocity between the belt and pulley periphery.

VA is
the Branch A linear velocity.

VB is
the Branch B linear velocity.

ωS is
the pulley angular velocity.

R is
the pulley radius.

FC is
the belt centrifugal force.

ρ is
the belt linear density.

Ffr is
the friction force between the pulley and the belt.

FA is the
force acting along branch A.

FB is the
force acting along branch B.

f is the friction coefficient.

θ is the contact wrap angle.

For a flat band, specify the value of f directly
in the block parameters dialog box. For a V-belt, the model calculates
the value using this equation:

f' is the effective
friction coefficient for a V-belt.

Φ is
the V-belt sheave angle.

The idealization of the discontinuity at Vrel =
0 is both difficult for the solver to resolve and not completely physically
accurate. To alleviate this issue, the friction coefficient is assumed
to change its value as a function of the relative velocity, with the
following relationship:

μ is
the instantaneous value of the friction coefficient.

f is
the steady-state value of the friction coefficient.

Vthr is
the friction velocity threshold.

The friction velocity threshold controls the width of the region
within which the friction coefficient changes its value from zero
to a steady-state maximum. The friction velocity threshold specifies
the velocity at which the hyperbolic tangent equals 0.999. The smaller
the value, the steeper is the change of μ.

This parameter uses the following equation to calculate the
friction force:

The resulting torque on the pulley is given by the following
equation:

TS is
the pulley torque.

b is
the bearing viscous damping.

The block equations model power transmission between the belt
branches or to/from the pulley. The tight and loose branches use the
same calculation. Without sufficient tension, the frictional force
is not enough to transmit power between the pulley and belt.

The model is valid when both ends of the belt are in tension.
An optional warning can display at the MATLAB® command line when
either belt end loses tension. When assembling a model, ensure that
tension is maintained throughout the simulation. Interpret the results
with this in mind.

Connection S is a conserving rotational terminal associated
with the pulley shaft. Connections A and B are the conserving mechanical
translational ports associated with the belt ends. The sign convention
is such that a positive rotation in port S tends to give a negative
translation for port A and a positive translation for port B.

Assumptions and Limitations

The model does not account for compliance along the
length of the belt.

Both belt ends maintain adequate tension throughout
the simulation.

Dialog Box and Parameters

Belt

Belt type

Type of flexible element modeled.

Flat band — (Default)

V-belt— Exposes
the V-belt sheave angle and Number
of V-belts parameters.

V-belt sheave angle

Sheave angle of the V-belt. Default is 30 deg.

The V-belt sheave angle parameter is visible
only when the Belt type parameter is V-belt.

Number of V-belts

Number of parallel V-belts. The default value is 1.

Non-integer values are rounded to the nearest integer. Increasing
the number of belts increases the friction force, effective mass per
unit length, and maximum allowable tension. Non-integer values are
rounded to the nearest integer.

The Number of V-belts parameter is visible
only when the Belt type parameter is V-belt.

Belt mass per unit length

Linear density of each belt. Default is 0.6 kg/m.

The model uses this parameter to calculate the centrifugal loading.

Belt direction

Relative direction of translational motion of one belt end with
respect to the other. Options include:

Ends move in opposite direction

Ends move in same direction

Maximum tension

Specifies whether the block throws an assertion when the belt
tension is too large.

The Pulley inertia parameter is visible
only when the Inertia parameter is Specify
inertia and initial velocity.

Pulley initial velocity

Initial rotational velocity of the pulley. Default is 0
rad/s.

The Pulley initial velocity parameter is
visible only when the Inertia parameter is Specify
inertia and initial velocity.

Use the Contact pane to specify contact
characteristics.

Contact

Contact friction coefficient

Coulomb friction coefficient between the belt and the pulley
surface. Default is 0.5.

Wrap angle

Angle of contact between the belt and pulley. Default is 180
deg.

Friction velocity threshold

Relative velocity required for peak kinetic friction in the
contact. The friction velocity threshold improves the numerical stability
of the simulation by ensuring that the force is continuous when the
direction of the velocity changes. Default is 0.001 m/s.